An instructor gives her class a set of 10 porblems with the information that the final exam will consist of a random selection of 5 of them. If a student has figured out how to do 7 of the the problems, what is the probability that the student will answer correctly
a) all 5 problems?
b) at least 4 of the problems?
Hello, r7iris!
I think I've worked it out . . .
An instructor gives her class a set of 10 problems with the information
that the final exam will consist of a random selection of 5 of them.
If a student has figured out how to do 7 of the the problems,
what is the probability that the student will answer correctly
(a) all 5 problems?
(b) at least 4 of the problems?
(a) It doesn't matter which five problems the instructor picks.
We are concerned with whether the student's seven prepared solutions
. . include the five problems.
There are: . ways that the student can choose 7 problems.
To get all 5 problems correct, his 7 preparations must include:
. . the 5 problems chosen by the instructor (one way),
. . and any 2 of the other 5 problems: . ways.
Hence, he has: . ways to get all 5 problems correct.
Therefore: .
(b) To get 4 or 5 problems correct . . .
We already know there are ways to get 5 correct.
To get 4 correct, he must choose:
. . 4 of the chosen 5 problems: . ways.
. . and 3 from the other five: . ways.
Hence, he has: . ways to get 4 correct.
Therefore, he has: . ways to get 4 or 5 correct
. . and: .